variational_form / weak_form / functional TODO list

[samuelpmishLLNL]

Originally from the PR, this is a TODO list to track priorities and development progress. It will be regularly updated as new features are completed.

To-do list:

(1: high priority, 5: low priority) (✔️: written and working, ⁉️: some development, but untested or not working, ❌: not started)

Function Spaces

	H1	Hcurl	Hdiv	DG
Triangles	⁉️ (4)	⁉️ (4)	❌(5)	⁉️ (4)
Quadrilaterals	✔️	✔️	❌(4)	✔️
Tetrahedra	⁉️ (3)	⁉️ (3)	❌(5)	⁉️ (3)
Hexahedra	✔️	✔️	❌(4)	✔️

Domains of Integration (see picture below)

	1	2	3
1D	❌(4-5)	n/a	n/a
2D	✔️	✔️	n/a
3D	❌(4)	✔️	✔️

• ❌ flux-type element calculations over all interfaces between neighboring elements (4-5)
• ❌ contact surfaces (4-5)

Functional features

• ✔️ kernel template: residual evaluation w/ automatic differentiation
• ✔️ kernel template: action of gradient
• ✔️ kernel template: assemble gradient matrix
• ❌ support with scalar or tensor valued arguments (e.g. make time available to q-function) (3)
• ✔️ support QoIs for case where test space == double
• ✔️ kernel template: assemble gradient vector (QoI)
• ✔️ implement some basic material models for different physics
• ✔️ allow user-defined types to be passed in to certain integrals (e.g. material state for plasticity models)
• ⁉️ allow user-defined annotations on integrals (e.g. only provide temperature gradient for this element calculation) (4)
• ✔️ multiphysics support (i.e. support more than 1 trial space per weak form)

Tensor / Dual Number Classes

• ✔️ base implementation of statically sized tensor class, and dual number/tensor classes
• ✔️ support arithmetic on tuples of tensors / dual numbers
• ✔️ support differentiation of functions with multiple inputs/outputs
• ✔️ automatically detect if an output does not depend on certain inputs, and optimize out derivative calculation
• ⁉️ automatically detect if an output is linear / nonlinear, and cache derivatives accordingly (4)
• ⁉️ automatically detect symmetries (isotropy, orthotropy, symmetry, antisymmetry, etc) in outputs and store accordingly (4-5)
• ✔️ support evaluation/differentiation of advanced tensor functions (inv, det, polar_decomposition, etc)

Performance Testing

• ✔️ profile existing tensor / dual number classes
• ✔️ profile shape function value / gradient
• ⁉️ profile common kernels (diffusion, mass, etc) (3-4)
• ✔️ profile high-level residual evaluation
• ⁉️ run/profile each of the above on CUDA as well (1-2)
• ✔️ investigate performance benefits of alternative implementations

[jamiebramwell]

@samuelpmishLLNL , is this up to date?

[samuelpmishLLNL]

updated list to current status

[samuelpmishLLNL]

it might be worth updating the triage for the remaining items, too